Middle School Science Quiz: Compare Potential Energy
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Compare Potential EnergyQuestion 1 of 20

A hiker of mass mm climbs from Position A at h=100 mh=100\,\text{m} to Position B at h=160 mh=160\,\text{m}. What expression gives the change in gravitational potential energy from A to B?

ΔPE=mg(100−160)\Delta PE = mg(100-160)
ΔPE=mg(160−100)\Delta PE = mg(160-100)
ΔPE=m(g−60)\Delta PE = m(g-60)
ΔPE=(mg)(160)(100)\Delta PE = (mg)(160)(100)
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Middle School Science Quiz

Middle School Science Quiz: Compare Potential Energy

Practice Compare Potential Energy in Middle School Science with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Compare Potential Energy, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Science.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

A hiker of mass mm climbs from Position A at h=100 mh=100\,\text{m} to Position B at h=160 mh=160\,\text{m}. What expression gives the change in gravitational potential energy from A to B?

  1. ΔPE=mg(100−160)\Delta PE = mg(100-160)
  2. ΔPE=mg(160−100)\Delta PE = mg(160-100) (correct answer)
  3. ΔPE=m(g−60)\Delta PE = m(g-60)
  4. ΔPE=(mg)(160)(100)\Delta PE = (mg)(160)(100)
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. For this upward motion of the hiker: Climbing from h = 100 m to h = 160 m, the change is ΔPE = mg(160 - 100) = mg*60 (positive), representing the energy stored by gaining height, which could be converted back if descending. Choice B is correct because it gives ΔPE = mg(160-100), correctly using final minus initial height for the positive change in upward motion. Choice A is wrong because it reverses the order to mg(100-160) = negative, which would be for descending; choice D uses product (mg)(160)(100), not difference; choice C misuses g-60, ignoring height difference properly. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications include mountain climbing where hikers gain PE that relates to caloric expenditure and pumped storage hydropower where water is pumped to higher elevations to store PE.

Question 2

A box is lifted straight up from a shelf at h=1 mh=1\,\text{m} to a higher shelf at h=4 mh=4\,\text{m}. Which expression gives the box's change in gravitational potential energy?

  1. ΔPE=mg(1−4)\Delta PE = mg(1-4)
  2. ΔPE=mg(4−1)\Delta PE = mg(4-1) (correct answer)
  3. ΔPE=mg(4+1)\Delta PE = mg(4+1)
  4. ΔPE=mg(4−1)\Delta PE = \dfrac{m}{g}(4-1)
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. As the box is lifted from the lower shelf (h = 1 m) to the higher shelf (h = 4 m), its gravitational potential energy increases: PEinitial = mg(1), PEfinal = mg(4), so ΔPE = PEfinal - PEinitial = mg(4) - mg(1) = mg(4-1) = 3mg—the positive change reflects energy added by lifting against gravity. Choice B is correct because it gives ΔPE = mg(4-1), properly expressing the change in PE as final minus initial heights multiplied by mg, which equals mg(3) = 3mg for the upward motion. Choice A reverses the subtraction mg(1-4), giving negative result for upward motion; Choice C adds heights mg(4+1) instead of finding the difference; Choice D incorrectly divides m by g instead of multiplying. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Warehouse forklifts demonstrate this daily: lifting boxes to high shelves requires work (adding PE = mgΔh), which represents stored energy that could be dangerous if boxes fall—safety protocols exist because that stored PE would convert to destructive KE in a fall.

Question 3

A box is moved between two shelves. Shelf A is at height h=1 mh=1\text{ m} and Shelf B is at height h=4 mh=4\text{ m} (measured from the floor). Which shelf gives the box greater gravitational potential energy, and why?

  1. Shelf A, because being closer to the ground increases gravitational potential energy.
  2. Shelf B, because gravitational potential energy increases with height (PE=mghPE=mgh). (correct answer)
  3. They are the same, because gravitational potential energy depends only on mass.
  4. Shelf A, because moving upward makes potential energy decrease.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. For static positions on shelves: Shelf A at h=1 m has PE = mg(1), while Shelf B at h=4 m has PE = mg(4), so Shelf B has greater PE by mg(3) due to the higher position—this stored energy difference means the box on B could release more energy if falling to the floor (converting to more KE). The comparison highlights that PE is directly proportional to height for a given mass and g, with the floor as reference (h=0). Choice B is correct because gravitational potential energy increases with height (PE=mgh), so higher shelf B has greater PE. Choice A reverses the relationship: claims closer to ground increases PE, opposite of PE = mgh; Choice C claims same because only mass matters, ignoring h; Choice D says upward decreases PE, again reversed. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications: (1) hydroelectric dams store water at height (high PE), release it to fall (PE → KE → turbine rotation → electricity), (2) pumped storage: pump water uphill when electricity cheap (store as PE), release downhill when electricity needed (PE → KE → generate electricity), (3) roller coasters: lift cart to top (add PE), release (PE → KE creating speed for thrilling ride), (4) trebuchets/catapults: raise counterweight (store PE), release (PE → KE → projectile motion).

Question 4

An object of mass mm moves from Position A at height h=8 mh=8\,\text{m} to Position B at height h=2 mh=2\,\text{m}. What is the change in gravitational potential energy, ΔPE=PEB−PEA\Delta PE = PE_B - PE_A?

  1. ΔPE=mg(8−2)=+6mg\Delta PE = mg(8-2)=+6mg
  2. ΔPE=mg(2−8)=−6mg\Delta PE = mg(2-8)=-6mg (correct answer)
  3. ΔPE=mg(2+8)=10mg\Delta PE = mg(2+8)=10mg
  4. ΔPE=mg(8×2)=16mg\Delta PE = mg(8\times 2)=16mg
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. For the object: From h=8 m (PE=mg(8)) to h=2 m (PE=mg(2)), ΔPE=mg(2-8)=-6mg, negative because height decreased. Choice B is correct because it properly calculates ΔPE = mgΔh for the position change with the correct negative sign and magnitude. Choice A has wrong positive sign as if ascending; Choice C adds heights incorrectly; Choice D multiplies heights wrongly. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications include falling objects, where negative ΔPE corresponds to KE gain, like in waterfalls generating power.

Question 5

A rock is dropped from a cliff at h=12 mh=12\text{ m} above the ground (take ground as h=0h=0). As the rock falls toward the ground, what happens to its gravitational potential energy?

  1. It increases because the rock speeds up.
  2. It decreases because height is decreasing. (correct answer)
  3. It stays constant because gravity is constant.
  4. It becomes greatest at the ground because the rock is moving fastest there.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. As the rock falls from the cliff (h = 12 m) toward the ground (h = 0 m), its height continuously decreases, so its gravitational potential energy decreases from PEinitial = mg(12) = 12mg J toward PEfinal = mg(0) = 0 J—the rock loses PE = 12mg J during the fall, with this energy converting to kinetic energy as the rock accelerates downward. The PE decreases smoothly and continuously during the fall: at h = 9 m it has PE = 9mg (lost 3mg), at h = 6 m it has PE = 6mg (lost 6mg), at h = 3 m it has PE = 3mg (lost 9mg), until reaching ground where all 12mg J of initial PE has converted to KE. Choice B is correct because it accurately states PE decreases as height decreases during the fall, following the fundamental PE = mgh relationship where falling means h decreases so PE decreases. Choice A confuses PE and KE: claims PE increases because rock speeds up, when actually speeding up means KE increases while PE decreases; Choice C incorrectly claims PE stays constant because gravity is constant, ignoring that PE = mgh changes with height h even though g is constant; Choice D reverses the relationship, claiming PE is greatest at ground where rock moves fastest, when actually PE = 0 at ground (h = 0) and KE is maximum there. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). This principle explains falling object behavior: dropped items accelerate because PE converts to KE, meteorites gain tremendous speed falling through atmosphere as enormous PE (from space altitude) becomes KE, and base jumpers rely on PE at cliff top converting to KE during freefall before parachute deployment.

Question 6

A person of mass mm climbs stairs from the first floor (h=0 mh=0\text{ m}) to the second floor (h=3 mh=3\text{ m}) and then to the third floor (h=6 mh=6\text{ m}). How does the person's gravitational potential energy change from the first floor to the third floor?

  1. It increases by ΔPE=mg(6−0)=6mg\Delta PE = mg(6-0)=6mg because height increases. (correct answer)
  2. It decreases by 6mg6mg because the person is moving upward.
  3. It stays the same because mass mm does not change.
  4. It increases only from the first to the second floor, then stays constant from the second to the third floor.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. As the person climbs from the first floor (h = 0 m, reference point where PE = 0) to the third floor (h = 6 m), their gravitational potential energy increases from PE₀ = mg(0) = 0 J to PEfinal = mg(6) = 6mg J—the person gained ΔPE = PEfinal - PEinitial = 6mg - 0 = +6mg J during the climb, which represents the work done against gravity to lift them (work = force × distance = mg × 6 m = same 6mg J). Choice A is correct because it accurately states PE increases by ΔPE = mg(6-0) = 6mg when the person rises from h = 0 to h = 6 m, properly using the formula ΔPE = mgΔh with positive Δh for upward motion. Choice B reverses the relationship: claims PE decreases when moving upward, opposite of the actual PE = mgh relationship where PE increases with height; Choice C incorrectly claims PE doesn't change, ignoring that PE depends on height h, not just mass m; Choice D wrongly suggests PE stops changing after the second floor, when actually PE continues to increase as height increases to the third floor. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications include hydroelectric dams storing water at height (high PE) to release for electricity generation, and even everyday activities like climbing stairs where you do work against gravity to increase your PE, storing energy that could be released if you jumped down.

Question 7

A pendulum bob is 0.5 m0.5\,\text{m} above its lowest point at the left endpoint, passes through the lowest point (h=0h=0), and reaches 0.5 m0.5\,\text{m} above the lowest point at the right endpoint. Using PE=mghPE=mgh with the lowest point as the reference, how does the bob's gravitational potential energy change during one swing from left endpoint to bottom to right endpoint?

  1. High → zero → high (it decreases to the bottom, then increases again). (correct answer)
  2. Zero → high → zero.
  3. It stays constant because the bob returns to the same height.
  4. Low → lower → lowest.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. Moving upward increases PE (climbing stairs, lifting object, rising elevator all gain gravitational PE as they gain height), while moving downward decreases PE (falling, descending, lowering all lose gravitational PE as they lose height), with the change in PE calculated as ΔPE = mg(hfinal - hinitial) = mgΔh (positive if going up, negative if going down). For the pendulum bob: Starting at left endpoint (h = 0.5 m above lowest point), PE = mg(0.5) = 0.5mg J (high PE); swinging down to lowest point (h = 0, reference), PE = mg(0) = 0 J (zero PE at bottom); continuing up to right endpoint (h = 0.5 m again), PE = mg(0.5) = 0.5mg J (high PE again)—the pattern is high → zero → high as the bob swings through one complete swing. Choice A is correct because it accurately describes PE changes: high at left endpoint (0.5 m up), decreases to zero at bottom (h = 0), then increases back to high at right endpoint (0.5 m up again). Choice B reverses the pattern (zero → high → zero would mean starting at bottom), Choice C incorrectly claims PE stays constant (wrong—PE varies with height even though endpoints are same height), and Choice D suggests PE only decreases (wrong—PE increases again as bob rises to right endpoint). The pendulum demonstrates cyclic PE changes: PE is maximum at the endpoints where height is maximum (0.5 m), minimum at the bottom where height is zero, with smooth variation between—this PE converts to KE at bottom (fastest) and back to PE at endpoints (momentarily at rest).

Question 8

An elevator lifts a person of mass mm from the ground floor (Position A, h=0 mh=0\text{ m}) to the 10th floor (Position B, h=30 mh=30\text{ m}). Which expression correctly gives the increase in the person's gravitational potential energy?

  1. ΔPE=mg(0−30)\Delta PE = mg(0-30)
  2. ΔPE=mgh=mg⋅30 m\Delta PE = mgh = mg\cdot 30\text{ m} (correct answer)
  3. ΔPE=mg⋅30 m\Delta PE = \dfrac{m}{g}\cdot 30\text{ m}
  4. ΔPE=mg⋅10 m\Delta PE = mg\cdot 10\text{ m} because it goes to the 10th floor.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. Moving upward increases PE (climbing stairs, lifting object, rising elevator all gain gravitational PE as they gain height), while moving downward decreases PE (falling, descending, lowering all lose gravitational PE as they lose height), with the change in PE calculated as ΔPE = mg(hfinal - hinitial) = mgΔh (positive if going up, negative if going down). For this upward motion: As the person rises from ground level (h = 0 m, reference where PE = 0) to h = 30 m, their gravitational potential energy increases from PE₀ = mg(0) = 0 J to PEfinal = mg(30) = 30mg J—the person gained PE = 30mg J during the lift, which represents the work done by the elevator against gravity (work = mg × 30 m). Choice B is correct because it properly calculates ΔPE = mgh = mg·30 m for the position change (increase). Choice A has wrong sign: positive to negative, as if descending; Choice C uses wrong formula (m/g instead of mg); Choice D uses wrong height (10 m instead of 30 m). The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications: (1) hydroelectric dams store water at height (high PE), release it to fall (PE → KE → turbine rotation → electricity), (2) pumped storage: pump water uphill when electricity cheap (store as PE), release downhill when electricity needed (PE → KE → generate electricity), (3) roller coasters: lift cart to top (add PE), release (PE → KE creating speed for thrilling ride), (4) trebuchets/catapults: raise counterweight (store PE), release (PE → KE → projectile motion).

Question 9

A cart moves on a track through three labeled positions shown below: Position A at h=0 mh=0\,\text{m}, Position B at h=8 mh=8\,\text{m}, and Position C at h=0 mh=0\,\text{m}. Ignoring friction, at which position(s) is the cart's gravitational potential energy the same?

  1. Only at Position B
  2. Only at Position A
  3. Positions A and C (correct answer)
  4. Positions A, B, and C
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases, and is the same at equal heights. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. For this cart motion on the track: At Positions A and C (both h = 0 m, PE = mg0 = 0), PE is the same (minimum), while at Position B (h = 8 m, PE = mg8, maximum), it's higher; ignoring friction, PE depends only on height, so same h means same PE regardless of location on track. Choice C is correct because it identifies Positions A and C as having the same PE, accurately noting they share the same height (h=0 m). Choice D is wrong because it includes B, but B has different h (8 m) so different PE; choice A says only B, but B is unique; choice B says only A, ignoring C at same h. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications include roller coasters where multiple points at the same height have equal PE, allowing energy conservation analysis, and water reservoirs at equal elevations having the same PE per unit mass.

Question 10

A rock of mass 3 kg3\,\text{kg} falls from a cliff at h=12 mh=12\,\text{m} to a ledge at h=7 mh=7\,\text{m}. Using g≈10 m/s2g\approx 10\,\text{m/s}^2, what is the change in gravitational potential energy (ΔPE=PEfinal−PEinitial\Delta PE = PE_{\text{final}} - PE_{\text{initial}}) for this fall?

  1. ΔPE=+150 J\Delta PE = +150\,\text{J}
  2. ΔPE=−150 J\Delta PE = -150\,\text{J} (correct answer)
  3. ΔPE=−360 J\Delta PE = -360\,\text{J}
  4. ΔPE=0 J\Delta PE = 0\,\text{J}
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. Moving upward increases PE (climbing stairs, lifting object, rising elevator all gain gravitational PE as they gain height), while moving downward decreases PE (falling, descending, lowering all lose gravitational PE as they lose height), with the change in PE calculated as ΔPE = mg(hfinal - hinitial) = mgΔh (positive if going up, negative if going down). For the falling rock: starting at cliff top (h = 12 m) with PE_initial = mgh₁ = (3 kg)(10 m/s²)(12 m) = 360 J, falling to ledge (h = 7 m) with PE_final = mgh₂ = (3 kg)(10 m/s²)(7 m) = 210 J. The change in PE is ΔPE = PE_final - PE_initial = 210 J - 360 J = -150 J, or using the formula: ΔPE = mgΔh = (3)(10)(7-12) = (3)(10)(-5) = -150 J. The negative sign indicates PE decreased during the fall, with 150 J of PE converting to kinetic energy as the rock gains speed. Choice B is correct because it accurately calculates ΔPE = -150 J for the rock falling from h = 12 m to h = 7 m, with negative sign properly indicating PE decrease during downward motion. Choice A shows +150 J with wrong sign, suggesting PE increases when falling, opposite of actual behavior; Choice C calculates -360 J, which is negative of initial PE but not the change (would require falling to h = 0); Choice D claims no change (0 J), ignoring that height decreased from 12 m to 7 m which must decrease PE. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Falling objects demonstrate energy conversion: initial PE at height converts to KE during fall, with the 150 J lost from PE becoming 150 J gained in KE (rock speeds up)—understanding this helps predict impact: higher falls mean more PE to convert, thus higher impact speeds and forces.

Question 11

A skateboarder rolls down a ramp from a platform at h=4 mh=4\,\text{m} to the ground at h=0 mh=0\,\text{m}. Which statement correctly describes the skateboarder's gravitational potential energy during the descent?

  1. It increases because the skateboarder speeds up.
  2. It decreases because height decreases; potential energy is converted to other forms like kinetic energy. (correct answer)
  3. It stays the same because gravity is constant.
  4. It depends only on mass, so it cannot change during motion.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. Moving upward increases PE (climbing stairs, lifting object, rising elevator all gain gravitational PE as they gain height), while moving downward decreases PE (falling, descending, lowering all lose gravitational PE as they lose height), with the change in PE calculated as ΔPE = mg(hfinal - hinitial) = mgΔh (positive if going up, negative if going down). For the skateboarder descending: rolling from platform (h = 4 m) down to ground (h = 0 m), the gravitational potential energy decreases from PE₁ = mgh₁ = mg(4) = 4mg J to PE₂ = mg(0) = 0 J. The skateboarder loses PE = 4mg J during descent, with this lost PE converting to kinetic energy (speed increases) as they roll down—energy transforms from PE to KE while total energy remains constant. At the bottom, all the initial PE has become KE, making the skateboarder move fastest at the lowest point. Choice B is correct because it accurately states PE decreases as height decreases during descent and correctly identifies that this PE converts to other forms like kinetic energy—the complete explanation of energy transformation during the roll down. Choice A claims PE increases because speed increases, confusing cause and effect: speed increases because PE decreases and converts to KE, not the reverse; Choice C states PE stays same because gravity is constant, missing that PE = mgh changes when h changes even though g is constant; Choice D suggests PE depends only on mass and cannot change, ignoring the height dependence in PE = mgh. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Skateboard ramps perfectly demonstrate energy conversion: starting high with PE and no speed, rolling down converts PE → KE (gaining speed), reaching bottom with maximum KE and minimum PE—understanding this helps skaters judge speed: higher starting point means more PE to convert, thus higher speed at bottom.

Question 12

Two identical carts (same mass) are on different tracks. Cart A is at height h=8 mh=8\,\text{m} and Cart B is at height h=3 mh=3\,\text{m}, measured from the same reference level. Which comparison is correct for their gravitational potential energies?

  1. Cart B has more gravitational potential energy because it is closer to the ground.
  2. They have the same gravitational potential energy because their masses are the same.
  3. Cart A has more gravitational potential energy because it is at a greater height. (correct answer)
  4. Their gravitational potential energies depend on their speeds, not their heights.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. Moving upward increases PE (climbing stairs, lifting object, rising elevator all gain gravitational PE as they gain height), while moving downward decreases PE (falling, descending, lowering all lose gravitational PE as they lose height), with the change in PE calculated as ΔPE = mg(hfinal - hinitial) = mgΔh (positive if going up, negative if going down). For comparing the two carts: Cart A at h = 8 m has PE_A = mgh_A = mg(8) = 8mg J, while Cart B at h = 3 m has PE_B = mgh_B = mg(3) = 3mg J. Since both carts have identical mass m and experience same gravity g, the cart at greater height has more PE: PE_A = 8mg > PE_B = 3mg, with Cart A having 8mg - 3mg = 5mg J more potential energy than Cart B. The height difference alone determines the PE difference when masses are equal. Choice C is correct because it accurately states Cart A has more gravitational PE due to its greater height—at h = 8 m versus h = 3 m, Cart A has higher position in gravitational field and thus more stored energy. Choice A reverses the relationship, claiming Cart B (lower position) has more PE when actually lower height means less PE; Choice B incorrectly states equal PE just because masses are equal, ignoring that different heights give different PE even for same mass; Choice D suggests PE depends on speed rather than height, confusing kinetic energy (speed-dependent) with potential energy (position-dependent). The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). This comparison illustrates why height matters for energy storage: two identical objects at different heights have different energy potentials—the higher one could do more work if released (more PE to convert), which explains why water towers are built tall (more PE for water pressure) and why higher diving boards allow more spectacular dives (more PE → KE → athletic maneuvers).

Question 13

A person of mass mm climbs stairs from the first floor at h=0 mh=0\,\text{m} to the second floor at h=3 mh=3\,\text{m} and then to the third floor at h=6 mh=6\,\text{m}. How does the person's gravitational potential energy change from the first floor to the third floor (in terms of mm and taking g≈10 m/s2g\approx 10\,\text{m/s}^2)?

  1. It decreases by 60m J60m\,\text{J} because the person is moving upward.
  2. It increases by 60m J60m\,\text{J} because height increases and ΔPE=mgΔh\Delta PE = mg\Delta h. (correct answer)
  3. It stays the same because potential energy depends on speed, not height.
  4. It increases by 30m J30m\,\text{J} because the person only climbs one floor.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. Moving upward increases PE (climbing stairs, lifting object, rising elevator all gain gravitational PE as they gain height), while moving downward decreases PE (falling, descending, lowering all lose gravitational PE as they lose height), with the change in PE calculated as ΔPE = mg(hfinal - hinitial) = mgΔh (positive if going up, negative if going down). For the person climbing stairs: starting at first floor (h = 0 m, reference point where PE = 0), climbing to third floor (h = 6 m), the gravitational potential energy increases from PE₀ = mg(0) = 0 J to PEfinal = mg(6) = 60m J—the person gained ΔPE = mg(6-0) = 60m J during the climb, which represents the work done against gravity to lift their mass through 6 meters vertical distance. Choice B is correct because it accurately states PE increases by 60m J when climbing from h = 0 to h = 6 m, correctly applying ΔPE = mgΔh = m(10)(6-0) = 60m J. Choice A reverses the relationship: claims PE decreases when moving upward, opposite of actual PE = mgh relationship where climbing increases h and thus PE; Choice C incorrectly states PE depends on speed rather than height, confusing kinetic energy (½mv²) with potential energy (mgh); Choice D calculates incorrectly as 30m J, perhaps thinking only one floor matters when the question asks for total change from first to third floor. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications include hydroelectric dams storing water at height (high PE) then releasing it to fall (PE → KE → turbine rotation → electricity), and even everyday activities like climbing stairs where you do work against gravity to increase your PE, which could be recovered if you slide down (PE → KE).

Question 14

A box of mass 5 kg5\,\text{kg} is moved from a shelf at h=2 mh=2\,\text{m} to a higher shelf at h=6 mh=6\,\text{m}. Using g≈10 m/s2g\approx 10\,\text{m/s}^2, how much gravitational potential energy does the box gain?

  1. ΔPE=200 J\Delta PE = 200\,\text{J} (correct answer)
  2. ΔPE=300 J\Delta PE = 300\,\text{J}
  3. ΔPE=20 J\Delta PE = 20\,\text{J}
  4. ΔPE=−200 J\Delta PE = -200\,\text{J}
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. Moving upward increases PE (climbing stairs, lifting object, rising elevator all gain gravitational PE as they gain height), while moving downward decreases PE (falling, descending, lowering all lose gravitational PE as they lose height), with the change in PE calculated as ΔPE = mg(hfinal - hinitial) = mgΔh (positive if going up, negative if going down). For the box being lifted: moving from lower shelf (h = 2 m) to higher shelf (h = 6 m), the gravitational potential energy increases from PE₁ = mgh₁ = (5 kg)(10 m/s²)(2 m) = 100 J to PE₂ = mgh₂ = (5 kg)(10 m/s²)(6 m) = 300 J. The box gained ΔPE = PE₂ - PE₁ = 300 J - 100 J = 200 J during the lift, or using the formula directly: ΔPE = mgΔh = (5)(10)(6-2) = (5)(10)(4) = 200 J. This 200 J represents the work done to lift the box against gravity through 4 m vertical distance. Choice A is correct because it accurately calculates ΔPE = 200 J for the box moving from h = 2 m to h = 6 m: ΔPE = mgΔh = (5)(10)(4) = 200 J, representing the PE gain. Choice B calculates as 300 J, which is the final PE at h = 6 m but not the change (ignores initial PE of 100 J at h = 2 m); Choice C gives only 20 J, perhaps using wrong height change or calculation error; Choice D shows -200 J with negative sign, suggesting PE decreases when lifting up, opposite of actual behavior. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Warehouse operations demonstrate this: forklifts do work to place boxes on high shelves (adding PE = mgh), which represents stored energy that could be dangerous if boxes fall (PE → KE → damage)—understanding position determines PE helps explain safety protocols for high storage and why heavier items are typically stored lower (less PE if they fall).

Question 15

A roller coaster cart is at Position A (h=0 mh=0\text{ m}), then rises to Position B (h=15 mh=15\text{ m}), then drops to Position C (h=5 mh=5\text{ m}). Compared to Position B, what can you say about the cart's gravitational potential energy at Position C?

  1. It is greater at C because the cart is moving faster at C.
  2. It is smaller at C because the height is smaller at C. (correct answer)
  3. It is the same at C because the cart stayed on the same track.
  4. It is greater at C because the cart moved downward.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. For roller coaster motion: At bottom A (h=0), PE=0; climbs to B (h=15 m), PE increases to mg(15) (max here); then drops to C (h=5 m), PE decreases to mg(5) while KE increases (speeds up). Compared to B, at C the PE is smaller because h is smaller (5 m < 15 m), with the difference mg(10) converted to KE during the drop. Choice B is correct because it accurately states PE decreases when object falls (h decreases), so smaller at lower position C. Choice A confuses PE and KE: claims greater at C because faster, but speeding up means KE increases while PE decreases; Choice C claims same, ignoring height change; Choice D says greater at C despite downward motion, reversed. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications: (1) hydroelectric dams store water at height (high PE), release it to fall (PE → KE → turbine rotation → electricity), (2) pumped storage: pump water uphill when electricity cheap (store as PE), release downhill when electricity needed (PE → KE → generate electricity), (3) roller coasters: lift cart to top (add PE), release (PE → KE creating speed for thrilling ride), (4) trebuchets/catapults: raise counterweight (store PE), release (PE → KE → projectile motion).

Question 16

A student lifts a 3 kg3\text{ kg} backpack from the floor (Position A, h=0 mh=0\text{ m}) onto a desk (Position B, h=1.2 mh=1.2\text{ m}). Take g≈10 N/kgg\approx 10\text{ N/kg}. How much gravitational potential energy does the backpack gain?

  1. 36 J36\text{ J} (correct answer)
  2. 3.6 J3.6\text{ J}
  3. −36 J-36\text{ J}
  4. 12 J12\text{ J}
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. Moving upward increases PE (climbing stairs, lifting object, rising elevator all gain gravitational PE as they gain height), while moving downward decreases PE (falling, descending, lowering all lose gravitational PE as they lose height), with the change in PE calculated as ΔPE = mg(hfinal - hinitial) = mgΔh (positive if going up, negative if going down). For this upward motion: As the backpack is lifted from floor (h = 0 m, PE=0) to desk (h=1.2 m), it gains PE = mgΔh = 3101.2 = 36 J—this gain represents the work done by the student against gravity to raise it. Choice A is correct because it properly calculates ΔPE = 36 J for the position change. Choice B wrong magnitude (3.6 J too small, perhaps forgot to multiply correctly); Choice C wrong sign (negative, as if lowering); Choice D wrong value (12 J, maybe used wrong height or g). The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications: (1) hydroelectric dams store water at height (high PE), release it to fall (PE → KE → turbine rotation → electricity), (2) pumped storage: pump water uphill when electricity cheap (store as PE), release downhill when electricity needed (PE → KE → generate electricity), (3) roller coasters: lift cart to top (add PE), release (PE → KE creating speed for thrilling ride), (4) trebuchets/catapults: raise counterweight (store PE), release (PE → KE → projectile motion).

Question 17

A ball of mass 2 kg2\,\text{kg} is thrown straight upward. Take the hand as the reference level (h=0h=0). At the top of its path, the ball is at h=5 mh=5\,\text{m}. Using g≈10 m/s2g\approx 10\,\text{m/s}^2, what is the change in gravitational potential energy from the hand to the top?

  1. +100 J+100\,\text{J} (correct answer)
  2. −100 J-100\,\text{J}
  3. +25 J+25\,\text{J}
  4. 0 J0\,\text{J}
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. For this upward motion of a thrown ball: As the ball rises from the hand (h = 0 m, PE = mg0 = 0 J) to the top (h = 5 m, PE = 2105 = 100 J), its gravitational potential energy increases by ΔPE = mgΔh = 100 J (positive since going up), representing the initial kinetic energy converted to PE as it slows while gaining height. Choice A is correct because it properly calculates ΔPE = +100 J using ΔPE = mg(h_final - h_initial) = 210*5 = +100 J for the upward position change. Choice B is wrong because it gives -100 J, reversing the sign—it would be correct for descending, but here the ball is rising (Δh positive); choice D claims 0 J, ignoring the height change; choice C uses wrong magnitude (25 J, perhaps miscalculating Δh or g). The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications include trebuchets that raise counterweights to store PE for launching projectiles and sports like basketball where throwing upward stores PE that converts back to KE on descent.

Question 18

A rock falls from a cliff top at h=12 mh=12\,\text{m} (Position A) to a ledge at h=4 mh=4\,\text{m} (Position B). Which statement best describes what happens to the rock's gravitational potential energy during this fall?

  1. It increases because the rock speeds up.
  2. It decreases because the rock's height decreases. (correct answer)
  3. It stays the same because gravity is constant.
  4. It is greatest at the lowest point because that is where the rock is moving fastest.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. For this downward motion of the falling rock: From cliff top (h = 12 m) to ledge (h = 4 m), PE decreases as height decreases (Δh = -8 m, ΔPE negative), with the lost PE converting to kinetic energy as the rock speeds up during the fall. Choice B is correct because it states PE decreases because the rock's height decreases, properly connecting the position change to the PE change via PE = mgh. Choice A is wrong because it claims PE increases as the rock speeds up, confusing PE with KE (speeding up means KE increases, while PE decreases); choice C says stays the same because gravity constant, but g constant doesn't prevent PE change with h; choice D incorrectly states greatest PE at lowest point due to fastest speed, but PE is least at lowest h, while speed (KE) is greatest there. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications include rockslides where high PE at cliffs converts to destructive KE and meteor impacts demonstrating extreme PE release from high altitudes.

Question 19

A roller coaster cart moves through these heights above the lowest point: bottom (Position A, h=0 mh=0\,\text{m}), top of a hill (Position B, h=20 mh=20\,\text{m}), and halfway down (Position C, h=10 mh=10\,\text{m}). Which comparison of gravitational potential energy is correct? (Use PE=mghPE=mgh.)

  1. PEA>PEC>PEBPE_A > PE_C > PE_B
  2. PEB>PEC>PEAPE_B > PE_C > PE_A (correct answer)
  3. PEC>PEB>PEAPE_C > PE_B > PE_A
  4. PEA=PEB=PECPE_A = PE_B = PE_C because the cart stays on the same track.
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. For this roller coaster motion: At the bottom (Position A, h = 0 m), PE = mg0 = 0 (minimum); at the top of the hill (Position B, h = 20 m), PE = mg20 (maximum); halfway down (Position C, h = 10 m), PE = mg*10 (intermediate); thus, the PE order is PE_B > PE_C > PE_A, as PE varies directly with height throughout the ride, with highest PE at the highest position and lowest at the lowest. Choice B is correct because it accurately states PE_B > PE_C > PE_A, properly connecting the positions' heights to their PE values using PE = mgh. Choice D is wrong because it claims PE is equal at all positions since the cart stays on the track, but PE changes with vertical position (height) even on the same track; choice A reverses the order, claiming PE_A (lowest h) is greatest, opposite of PE = mgh; choice C incorrectly orders PE_C > PE_B, putting intermediate height above the maximum. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). Applications include roller coasters: lift cart to top (add PE), release (PE → KE creating speed for thrilling ride), and pumped storage systems that pump water uphill to store PE for later electricity generation.

Question 20

A rock of mass 3 kg3\,\text{kg} falls from a cliff at height h=12 mh=12\,\text{m} to a ledge at height h=4 mh=4\,\text{m} (same reference level for both heights). Using g≈10 m/s2g\approx 10\,\text{m/s}^2, what is the change in gravitational potential energy, ΔPE=PEfinal−PEinitial\Delta PE = PE_{\text{final}}-PE_{\text{initial}}?

  1. +240 J+240\,\text{J}
  2. −240 J-240\,\text{J} (correct answer)
  3. +360 J+360\,\text{J}
  4. −360 J-360\,\text{J}
Explanation: This question tests understanding that gravitational potential energy changes as an object's position changes vertically—specifically, that PE increases with height and decreases when height decreases. Position in Earth's gravitational field determines gravitational potential energy through the height variable in PE = mgh: when an object is at higher position (larger h), it has more gravitational PE because h is larger (more energy stored), and when at lower position (smaller h), it has less PE. As the rock falls from the cliff (h = 12 m) to the ledge (h = 4 m), its gravitational potential energy decreases: PEinitial = mg(12) = (3 kg)(10 m/s²)(12 m) = 360 J; PEfinal = mg(4) = (3 kg)(10 m/s²)(4 m) = 120 J; so ΔPE = PEfinal - PEinitial = 120 J - 360 J = -240 J—the negative sign indicates PE decreased as the rock fell to lower position. Choice B is correct because it gives ΔPE = -240 J, accurately calculating the negative change in PE when falling from h = 12 m to h = 4 m, with the negative sign properly indicating a decrease in PE during downward motion. Choice A has wrong sign (+240 J), suggesting PE increases when falling; Choices C and D use 360 J instead of the actual change of 240 J, with C having wrong sign (+) and D having correct sign (-) but wrong magnitude. The position-PE connection is fundamental to understanding gravitational potential energy: (1) PE is energy of position (where you are in gravitational field matters), (2) higher positions have more PE (climbing stores energy by increasing h), (3) lower positions have less PE (descending releases energy by decreasing h), and (4) PE can convert to other forms (primarily KE when falling: PE → KE maintains total energy). When the rock falls, the 240 J of lost PE converts to kinetic energy, making the rock speed up as it falls—this PE → KE conversion powers everything from waterfalls to meteorite impacts.